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#ifndef PCL_REGISTRATION_NDT_OMP_H_
#define PCL_REGISTRATION_NDT_OMP_H_

#include <pcl/registration/registration.h>
#include <pcl/search/impl/search.hpp>
#include "voxel_grid_covariance_omp.h"

#include <unsupported/Eigen/NonLinearOptimization>

namespace pclomp {
enum NeighborSearchMethod {
  KDTREE,
  DIRECT26,
  DIRECT7,
  DIRECT1
};

/** \brief A 3D Normal Distribution Transform registration implementation for point cloud data.
  * \note For more information please see
  * <b>Magnusson, M. (2009). The Three-Dimensional Normal-Distributions Transform —
  * an Efﬁcient Representation for Registration, Surface Analysis, and Loop Detection.
  * PhD thesis, Orebro University. Orebro Studies in Technology 36.</b>,
  * <b>More, J., and Thuente, D. (1994). Line Search Algorithm with Guaranteed Sufficient Decrease
  * In ACM Transactions on Mathematical Software.</b> and
  * Sun, W. and Yuan, Y, (2006) Optimization Theory and Methods: Nonlinear Programming. 89-100
  * \note Math refactored by Todor Stoyanov.
  * \author Brian Okorn (Space and Naval Warfare Systems Center Pacific)
  */
template<typename PointSource, typename PointTarget>
class NormalDistributionsTransform : public pcl::Registration<PointSource, PointTarget> {
 protected:

  typedef typename pcl::Registration<PointSource, PointTarget>::PointCloudSource PointCloudSource;
  typedef typename PointCloudSource::Ptr PointCloudSourcePtr;
  typedef typename PointCloudSource::ConstPtr PointCloudSourceConstPtr;

  typedef typename pcl::Registration<PointSource, PointTarget>::PointCloudTarget PointCloudTarget;
  typedef typename PointCloudTarget::Ptr PointCloudTargetPtr;
  typedef typename PointCloudTarget::ConstPtr PointCloudTargetConstPtr;

  typedef pcl::PointIndices::Ptr PointIndicesPtr;
  typedef pcl::PointIndices::ConstPtr PointIndicesConstPtr;

  /** \brief Typename of searchable voxel grid containing mean and covariance. */
  typedef pclomp::VoxelGridCovariance<PointTarget> TargetGrid;
  /** \brief Typename of pointer to searchable voxel grid. */
  typedef TargetGrid *TargetGridPtr;
  /** \brief Typename of const pointer to searchable voxel grid. */
  typedef const TargetGrid *TargetGridConstPtr;
  /** \brief Typename of const pointer to searchable voxel grid leaf. */
  typedef typename TargetGrid::LeafConstPtr TargetGridLeafConstPtr;

 public:

  typedef boost::shared_ptr<NormalDistributionsTransform<PointSource, PointTarget> > Ptr;
  typedef boost::shared_ptr<const NormalDistributionsTransform<PointSource, PointTarget> > ConstPtr;

  /** \brief Constructor.
    * Sets \ref outlier_ratio_ to 0.35, \ref step_size_ to 0.05 and \ref resolution_ to 1.0
    */
  NormalDistributionsTransform();

  /** \brief Empty destructor */
  virtual ~NormalDistributionsTransform() {}

  void setNumThreads(int n) {
    num_threads_ = n;
  }

  /** \brief Provide a pointer to the input target (e.g., the point cloud that we want to align the input source to).
    * \param[in] cloud the input point cloud target
    */
  inline void
  setInputTarget(const PointCloudTargetConstPtr &cloud) {
    pcl::Registration<PointSource, PointTarget>::setInputTarget(cloud);
    init();
  }

  /** \brief Set/change the voxel grid resolution.
    * \param[in] resolution side length of voxels
    */
  inline void
  setResolution(float resolution) {
    // Prevents unnessary voxel initiations
    if (resolution_ != resolution) {
      resolution_ = resolution;
      if (input_)
        init();
    }
  }

  /** \brief Get voxel grid resolution.
    * \return side length of voxels
    */
  inline float
  getResolution() const {
    return (resolution_);
  }

  /** \brief Get the newton line search maximum step length.
    * \return maximum step length
    */
  inline double
  getStepSize() const {
    return (step_size_);
  }

  /** \brief Set/change the newton line search maximum step length.
    * \param[in] step_size maximum step length
    */
  inline void
  setStepSize(double step_size) {
    step_size_ = step_size;
  }

  /** \brief Get the point cloud outlier ratio.
    * \return outlier ratio
    */
  inline double
  getOulierRatio() const {
    return (outlier_ratio_);
  }

  /** \brief Set/change the point cloud outlier ratio.
    * \param[in] outlier_ratio outlier ratio
    */
  inline void
  setOulierRatio(double outlier_ratio) {
    outlier_ratio_ = outlier_ratio;
  }

  inline void setNeighborhoodSearchMethod(NeighborSearchMethod method) {
    search_method = method;
  }

  /** \brief Get the registration alignment probability.
    * \return transformation probability
    */
  inline double
  getTransformationProbability() const {
    return (trans_probability_);
  }

  /** \brief Get the number of iterations required to calculate alignment.
    * \return final number of iterations
    */
  inline int
  getFinalNumIteration() const {
    return (nr_iterations_);
  }

  /** \brief Convert 6 element transformation vector to affine transformation.
    * \param[in] x transformation vector of the form [x, y, z, roll, pitch, yaw]
    * \param[out] trans affine transform corresponding to given transfomation vector
    */
  static void
  convertTransform(const Eigen::Matrix<double, 6, 1> &x, Eigen::Affine3f &trans) {
    trans = Eigen::Translation<float, 3>(float(x(0)), float(x(1)), float(x(2))) *
        Eigen::AngleAxis<float>(float(x(3)), Eigen::Vector3f::UnitX()) *
        Eigen::AngleAxis<float>(float(x(4)), Eigen::Vector3f::UnitY()) *
        Eigen::AngleAxis<float>(float(x(5)), Eigen::Vector3f::UnitZ());
  }

  /** \brief Convert 6 element transformation vector to transformation matrix.
    * \param[in] x transformation vector of the form [x, y, z, roll, pitch, yaw]
    * \param[out] trans 4x4 transformation matrix corresponding to given transfomation vector
    */
  static void
  convertTransform(const Eigen::Matrix<double, 6, 1> &x, Eigen::Matrix4f &trans) {
    Eigen::Affine3f _affine;
    convertTransform(x, _affine);
    trans = _affine.matrix();
  }

  // negative log likelihood function
  // lower is better
  double calculateScore(const PointCloudSource &cloud) const;

 protected:

  using pcl::Registration<PointSource, PointTarget>::reg_name_;
  using pcl::Registration<PointSource, PointTarget>::getClassName;
  using pcl::Registration<PointSource, PointTarget>::input_;
  using pcl::Registration<PointSource, PointTarget>::indices_;
  using pcl::Registration<PointSource, PointTarget>::target_;
  using pcl::Registration<PointSource, PointTarget>::nr_iterations_;
  using pcl::Registration<PointSource, PointTarget>::max_iterations_;
  using pcl::Registration<PointSource, PointTarget>::previous_transformation_;
  using pcl::Registration<PointSource, PointTarget>::final_transformation_;
  using pcl::Registration<PointSource, PointTarget>::transformation_;
  using pcl::Registration<PointSource, PointTarget>::transformation_epsilon_;
  using pcl::Registration<PointSource, PointTarget>::converged_;
  using pcl::Registration<PointSource, PointTarget>::corr_dist_threshold_;
  using pcl::Registration<PointSource, PointTarget>::inlier_threshold_;

  using pcl::Registration<PointSource, PointTarget>::update_visualizer_;

  /** \brief Estimate the transformation and returns the transformed source (input) as output.
    * \param[out] output the resultant input transfomed point cloud dataset
    */
  virtual void
  computeTransformation(PointCloudSource &output) {
    computeTransformation(output, Eigen::Matrix4f::Identity());
  }

  /** \brief Estimate the transformation and returns the transformed source (input) as output.
    * \param[out] output the resultant input transfomed point cloud dataset
    * \param[in] guess the initial gross estimation of the transformation
    */
  virtual void
  computeTransformation(PointCloudSource &output, const Eigen::Matrix4f &guess);

  /** \brief Initiate covariance voxel structure. */
  void inline
  init() {
    target_cells_.setLeafSize(resolution_, resolution_, resolution_);
    target_cells_.setInputCloud(target_);
    // Initiate voxel structure.
    target_cells_.filter(true);
  }

  /** \brief Compute derivatives of probability function w.r.t. the transformation vector.
    * \note Equation 6.10, 6.12 and 6.13 [Magnusson 2009].
    * \param[out] score_gradient the gradient vector of the probability function w.r.t. the transformation vector
    * \param[out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
    * \param[in] trans_cloud transformed point cloud
    * \param[in] p the current transform vector
    * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
    */
  double
  computeDerivatives(Eigen::Matrix<double, 6, 1> &score_gradient,
                     Eigen::Matrix<double, 6, 6> &hessian,
                     PointCloudSource &trans_cloud,
                     Eigen::Matrix<double, 6, 1> &p,
                     bool compute_hessian = true);

  /** \brief Compute individual point contirbutions to derivatives of probability function w.r.t. the transformation vector.
    * \note Equation 6.10, 6.12 and 6.13 [Magnusson 2009].
    * \param[in,out] score_gradient the gradient vector of the probability function w.r.t. the transformation vector
    * \param[in,out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
    * \param[in] x_trans transformed point minus mean of occupied covariance voxel
    * \param[in] c_inv covariance of occupied covariance voxel
    * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
    */
  double
  updateDerivatives(Eigen::Matrix<double, 6, 1> &score_gradient,
                    Eigen::Matrix<double, 6, 6> &hessian,
                    const Eigen::Matrix<float, 4, 6> &point_gradient_,
                    const Eigen::Matrix<float, 24, 6> &point_hessian_,
                    const Eigen::Vector3d &x_trans, const Eigen::Matrix3d &c_inv,
                    bool compute_hessian = true) const;

  /** \brief Precompute anglular components of derivatives.
    * \note Equation 6.19 and 6.21 [Magnusson 2009].
    * \param[in] p the current transform vector
    * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
    */
  void
  computeAngleDerivatives(Eigen::Matrix<double, 6, 1> &p, bool compute_hessian = true);

  /** \brief Compute point derivatives.
    * \note Equation 6.18-21 [Magnusson 2009].
    * \param[in] x point from the input cloud
    * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
    */
  void
  computePointDerivatives(Eigen::Vector3d &x,
                          Eigen::Matrix<double, 3, 6> &point_gradient_,
                          Eigen::Matrix<double, 18, 6> &point_hessian_,
                          bool compute_hessian = true) const;

  void
  computePointDerivatives(Eigen::Vector3d &x,
                          Eigen::Matrix<float, 4, 6> &point_gradient_,
                          Eigen::Matrix<float, 24, 6> &point_hessian_,
                          bool compute_hessian = true) const;

  /** \brief Compute hessian of probability function w.r.t. the transformation vector.
    * \note Equation 6.13 [Magnusson 2009].
    * \param[out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
    * \param[in] trans_cloud transformed point cloud
    * \param[in] p the current transform vector
    */
  void
  computeHessian(Eigen::Matrix<double, 6, 6> &hessian,
                 PointCloudSource &trans_cloud,
                 Eigen::Matrix<double, 6, 1> &p);

  /** \brief Compute individual point contirbutions to hessian of probability function w.r.t. the transformation vector.
    * \note Equation 6.13 [Magnusson 2009].
    * \param[in,out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
    * \param[in] x_trans transformed point minus mean of occupied covariance voxel
    * \param[in] c_inv covariance of occupied covariance voxel
    */
  void
  updateHessian(Eigen::Matrix<double, 6, 6> &hessian,
                const Eigen::Matrix<double, 3, 6> &point_gradient_,
                const Eigen::Matrix<double, 18, 6> &point_hessian_,
                const Eigen::Vector3d &x_trans, const Eigen::Matrix3d &c_inv) const;

  /** \brief Compute line search step length and update transform and probability derivatives using More-Thuente method.
    * \note Search Algorithm [More, Thuente 1994]
    * \param[in] x initial transformation vector, \f$ x \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ \vec{p} \f$ in Algorithm 2 [Magnusson 2009]
    * \param[in] step_dir descent direction, \f$ p \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ \delta \vec{p} \f$ normalized in Algorithm 2 [Magnusson 2009]
    * \param[in] step_init initial step length estimate, \f$ \alpha_0 \f$ in Moore-Thuente (1994) and the noramal of \f$ \delta \vec{p} \f$ in Algorithm 2 [Magnusson 2009]
    * \param[in] step_max maximum step length, \f$ \alpha_max \f$ in Moore-Thuente (1994)
    * \param[in] step_min minimum step length, \f$ \alpha_min \f$ in Moore-Thuente (1994)
    * \param[out] score final score function value, \f$ f(x + \alpha p) \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ score \f$ in Algorithm 2 [Magnusson 2009]
    * \param[in,out] score_gradient gradient of score function w.r.t. transformation vector, \f$ f'(x + \alpha p) \f$ in Moore-Thuente (1994) and \f$ \vec{g} \f$ in Algorithm 2 [Magnusson 2009]
    * \param[out] hessian hessian of score function w.r.t. transformation vector, \f$ f''(x + \alpha p) \f$ in Moore-Thuente (1994) and \f$ H \f$ in Algorithm 2 [Magnusson 2009]
    * \param[in,out] trans_cloud transformed point cloud, \f$ X \f$ transformed by \f$ T(\vec{p},\vec{x}) \f$ in Algorithm 2 [Magnusson 2009]
    * \return final step length
    */
  double
  computeStepLengthMT(const Eigen::Matrix<double, 6, 1> &x,
                      Eigen::Matrix<double, 6, 1> &step_dir,
                      double step_init,
                      double step_max, double step_min,
                      double &score,
                      Eigen::Matrix<double, 6, 1> &score_gradient,
                      Eigen::Matrix<double, 6, 6> &hessian,
                      PointCloudSource &trans_cloud);

  /** \brief Update interval of possible step lengths for More-Thuente method, \f$ I \f$ in More-Thuente (1994)
    * \note Updating Algorithm until some value satifies \f$ \psi(\alpha_k) \leq 0 \f$ and \f$ \phi'(\alpha_k) \geq 0 \f$
    * and Modified Updating Algorithm from then on [More, Thuente 1994].
    * \param[in,out] a_l first endpoint of interval \f$ I \f$, \f$ \alpha_l \f$ in Moore-Thuente (1994)
    * \param[in,out] f_l value at first endpoint, \f$ f_l \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_l) \f$ for Update Algorithm and \f$ \phi(\alpha_l) \f$ for Modified Update Algorithm
    * \param[in,out] g_l derivative at first endpoint, \f$ g_l \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_l) \f$ for Update Algorithm and \f$ \phi'(\alpha_l) \f$ for Modified Update Algorithm
    * \param[in,out] a_u second endpoint of interval \f$ I \f$, \f$ \alpha_u \f$ in Moore-Thuente (1994)
    * \param[in,out] f_u value at second endpoint, \f$ f_u \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_u) \f$ for Update Algorithm and \f$ \phi(\alpha_u) \f$ for Modified Update Algorithm
    * \param[in,out] g_u derivative at second endpoint, \f$ g_u \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_u) \f$ for Update Algorithm and \f$ \phi'(\alpha_u) \f$ for Modified Update Algorithm
    * \param[in] a_t trial value, \f$ \alpha_t \f$ in Moore-Thuente (1994)
    * \param[in] f_t value at trial value, \f$ f_t \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_t) \f$ for Update Algorithm and \f$ \phi(\alpha_t) \f$ for Modified Update Algorithm
    * \param[in] g_t derivative at trial value, \f$ g_t \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_t) \f$ for Update Algorithm and \f$ \phi'(\alpha_t) \f$ for Modified Update Algorithm
    * \return if interval converges
    */
  bool
  updateIntervalMT(double &a_l, double &f_l, double &g_l,
                   double &a_u, double &f_u, double &g_u,
                   double a_t, double f_t, double g_t);

  /** \brief Select new trial value for More-Thuente method.
    * \note Trial Value Selection [More, Thuente 1994], \f$ \psi(\alpha_k) \f$ is used for \f$ f_k \f$ and \f$ g_k \f$
    * until some value satifies the test \f$ \psi(\alpha_k) \leq 0 \f$ and \f$ \phi'(\alpha_k) \geq 0 \f$
    * then \f$ \phi(\alpha_k) \f$ is used from then on.
    * \note Interpolation Minimizer equations from Optimization Theory and Methods: Nonlinear Programming By Wenyu Sun, Ya-xiang Yuan (89-100).
    * \param[in] a_l first endpoint of interval \f$ I \f$, \f$ \alpha_l \f$ in Moore-Thuente (1994)
    * \param[in] f_l value at first endpoint, \f$ f_l \f$ in Moore-Thuente (1994)
    * \param[in] g_l derivative at first endpoint, \f$ g_l \f$ in Moore-Thuente (1994)
    * \param[in] a_u second endpoint of interval \f$ I \f$, \f$ \alpha_u \f$ in Moore-Thuente (1994)
    * \param[in] f_u value at second endpoint, \f$ f_u \f$ in Moore-Thuente (1994)
    * \param[in] g_u derivative at second endpoint, \f$ g_u \f$ in Moore-Thuente (1994)
    * \param[in] a_t previous trial value, \f$ \alpha_t \f$ in Moore-Thuente (1994)
    * \param[in] f_t value at previous trial value, \f$ f_t \f$ in Moore-Thuente (1994)
    * \param[in] g_t derivative at previous trial value, \f$ g_t \f$ in Moore-Thuente (1994)
    * \return new trial value
    */
  double
  trialValueSelectionMT(double a_l, double f_l, double g_l,
                        double a_u, double f_u, double g_u,
                        double a_t, double f_t, double g_t);

  /** \brief Auxilary function used to determin endpoints of More-Thuente interval.
    * \note \f$ \psi(\alpha) \f$ in Equation 1.6 (Moore, Thuente 1994)
    * \param[in] a the step length, \f$ \alpha \f$ in More-Thuente (1994)
    * \param[in] f_a function value at step length a, \f$ \phi(\alpha) \f$ in More-Thuente (1994)
    * \param[in] f_0 initial function value, \f$ \phi(0) \f$ in Moore-Thuente (1994)
    * \param[in] g_0 initial function gradiant, \f$ \phi'(0) \f$ in More-Thuente (1994)
    * \param[in] mu the step length, constant \f$ \mu \f$ in Equation 1.1 [More, Thuente 1994]
    * \return sufficent decrease value
    */
  inline double
  auxilaryFunction_PsiMT(double a, double f_a, double f_0, double g_0, double mu = 1.e-4) {
    return (f_a - f_0 - mu * g_0 * a);
  }

  /** \brief Auxilary function derivative used to determin endpoints of More-Thuente interval.
    * \note \f$ \psi'(\alpha) \f$, derivative of Equation 1.6 (Moore, Thuente 1994)
    * \param[in] g_a function gradient at step length a, \f$ \phi'(\alpha) \f$ in More-Thuente (1994)
    * \param[in] g_0 initial function gradiant, \f$ \phi'(0) \f$ in More-Thuente (1994)
    * \param[in] mu the step length, constant \f$ \mu \f$ in Equation 1.1 [More, Thuente 1994]
    * \return sufficent decrease derivative
    */
  inline double
  auxilaryFunction_dPsiMT(double g_a, double g_0, double mu = 1.e-4) {
    return (g_a - mu * g_0);
  }

  /** \brief The voxel grid generated from target cloud containing point means and covariances. */
  TargetGrid target_cells_;

  //double fitness_epsilon_;

  /** \brief The side length of voxels. */
  float resolution_;

  /** \brief The maximum step length. */
  double step_size_;

  /** \brief The ratio of outliers of points w.r.t. a normal distribution, Equation 6.7 [Magnusson 2009]. */
  double outlier_ratio_;

  /** \brief The normalization constants used fit the point distribution to a normal distribution, Equation 6.8 [Magnusson 2009]. */
  double gauss_d1_, gauss_d2_, gauss_d3_;

  /** \brief The probability score of the transform applied to the input cloud, Equation 6.9 and 6.10 [Magnusson 2009]. */
  double trans_probability_;

  /** \brief Precomputed Angular Gradient
    *
    * The precomputed angular derivatives for the jacobian of a transformation vector, Equation 6.19 [Magnusson 2009].
    */
  Eigen::Vector3d j_ang_a_, j_ang_b_, j_ang_c_, j_ang_d_, j_ang_e_, j_ang_f_, j_ang_g_, j_ang_h_;

  Eigen::Matrix<float, 8, 4> j_ang;

  /** \brief Precomputed Angular Hessian
    *
    * The precomputed angular derivatives for the hessian of a transformation vector, Equation 6.19 [Magnusson 2009].
    */
  Eigen::Vector3d h_ang_a2_, h_ang_a3_,
      h_ang_b2_, h_ang_b3_,
      h_ang_c2_, h_ang_c3_,
      h_ang_d1_, h_ang_d2_, h_ang_d3_,
      h_ang_e1_, h_ang_e2_, h_ang_e3_,
      h_ang_f1_, h_ang_f2_, h_ang_f3_;

  Eigen::Matrix<float, 16, 4> h_ang;

  /** \brief The first order derivative of the transformation of a point w.r.t. the transform vector, \f$ J_E \f$ in Equation 6.18 [Magnusson 2009]. */
  //      Eigen::Matrix<double, 3, 6> point_gradient_;

  /** \brief The second order derivative of the transformation of a point w.r.t. the transform vector, \f$ H_E \f$ in Equation 6.20 [Magnusson 2009]. */
  //      Eigen::Matrix<double, 18, 6> point_hessian_;

  int num_threads_;

 public:
  NeighborSearchMethod search_method;

  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
};

}

#endif // PCL_REGISTRATION_NDT_H_
